To be honest, I tried to set Nominatim up on my virtual windows 10 machine.
But I have a feelin that I am doing wrong.

Does it make sense to install Nominatim locally on my windows and can I receive my goal with this?
If not, what hardware and OS would I need to get Nominatim working for my purpose?
Do I really need all Prerequisites from this site, or can I spare something out, because I only need lat / lon enrichment?
Is it really necessary to use a local installation of Nominatim, can I not use the web API of Nominatim to query lets say 100k adresses and receive lat / lon on a regular basis?

Yes you need all these prerequisites, and you cannot run it on Windows, you need to use a Linux VM. What you could do is install "photon" instead of Nominiatim, it's a different geocoder but it has the advantage that ready-made data downloads are available so you don't need to go through the data preparation steps. Being written in Java, it might even run on Windows:

You can definitely not download 100k addresses from OSM's Nominatim on a regular basis, but of course what you could do is find a commercial geocoding provider who runs Nominatim and lets you use that for a fee.

Also with regards to your "enriching" data, be advised that according to many people's interpretation the lat/lon data in your database will remain under the ODbL license and you might be required to share it on request. The exact application of the ODbL license to geocoding results is a topic under discussion.

Nice to hear a professional opinion, thank you.
Lets assume I would go for an Nominiatim installation on Linux VM and put the germany-latest.osm.pbf in it.
I want to extract as much lat / lon for adresses in germany as I want, in my humble imagination this is possible with a local setup as described above or with an photon installation, am I wrong?

So, when I install Nominiatim on a Linux VM on my laptop it can work as my own local server?

And just to be clear, with the above I can potentially enrich any adress from germany with lat / lon?

What do you mean with ready-made data downloads? The advantage of photon is not clear to me, the data preparation steps look equal, because with Nominiatim and photon i would query for certain adresses and get adress with lat / lon as result.
Can you tell me the difference?

Would be nice if you could answer me those 3 last things, cause then I can start working ;).

Yes it can work as your own local server, yes you can find the lat/lon for about 1/3 of addresses in Germany (the others aren't in OSM and you will get imprecise lat/lon e.g. same values for all addresses in one street etc), and when you use Photon you don't need a database or a data import because you can download a data file ready-made for use with Photon.